Page 274 - Soil and water contamination, 2nd edition

Gas exchange 261

After one half-life
C / H t
w
e L k 1/2 0
C
0
Thus,
ln( ) 2 ln( ) 2 5
t 1/2 . 4 33 10 s = 5.01 d
k L / H 4 . 2 10 6 5 . 1 /
This implies that half of the benzene has been volatilised after approximately 5 days.

14.3 REAERATION

In the case of oxygen exchange between surface water and the atmosphere, the term k /H in
L
Equation (14.11) is referred to as the reaeration constant k . The mass balance for exchange
r
of oxygen between surface water and the atmosphere is then:
dDO (14.13)
k r DO sat DO
dt
-3
where DO = dissolved oxygen concentration in surface water [M L ], DO = saturated
sat
-3
(equilibrium) dissolved oxygen concentration in surface water [M L ], and k = reaeration
r
-1
constant [T ]. The saturated dissolved oxygen concentration DO depends on the water
sat
temperature . The following empirical expression is commonly used to determine DO in mg
sat
-1
l as function of temperature (Lijklema, 1991):
DO 14 . 652 . 0 41022 T . 0 007991T 2 . 0 0000777774 T 3 (14.14)
sat
where T = the water temperature in °C.
Oxygen transfer across the air–water interface is controlled on the water side, because
the value of K’ is much larger than 0.01 (see Table 14.1). This means that the overall gas
H
exchange coefficient depends on the hydrodynamic characteristics of the air–water interface
and the flow regime. The surface renewal model – an alternative model for gas exchange
across the air–water interface – assumes that turbulent eddies bring small parcels of water
to the water surface. As long as these parcels are at the surface they can equilibrate with the
atmosphere. After equilibrium is reached, the chemical flux across the air–water interface
stops. If fresh parcels replace the depleted parcels more quickly, the flux becomes larger.
In deep flowing waters, the renewal rate in the mixing depth near the water surface is
approximately equal to the average flow velocity divided by the water depth. This assumption
leads to the O’Connor and Dobbins (1958) formula for estimation of the gas exchange
coefficient:

D u u (14.15)
k L w 3 .90
H H
-1
where u = the average flow velocity (m s ) and H = the water depth (m). The surface renewal
model thus assumes that the gas exchange coefficient is proportional to the square root of
the molecular diffusion coefficient in water D , in contrast to the thin film model , which
w
assumes that the gas exchange coefficient is proportional to D (see Equation 14.4). Besides
w
this theoretically derived Equation (14.15), a number of empirical relationships have been

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